scholarly journals Schauder bases and Köthe sequence spaces

1968 ◽  
Vol 130 (2) ◽  
pp. 265-265
Author(s):  
Ed Dubinsky ◽  
J. R. Retherford
Keyword(s):  
Sequence Spaces ◽  
Schauder Bases ◽  
Köthe Sequence Spaces

Schauder Bases and Kothe Sequence Spaces

1968 ◽  
Vol 130 (2) ◽  
pp. 265 ◽  
Author(s):  
Ed Dubinsky ◽  
J. R. Retherford
Keyword(s):  
Sequence Spaces ◽  
Schauder Bases ◽  
Köthe Sequence Spaces

On Köthe sequence spaces and linear logic

2002 ◽  
Vol 12 (5) ◽  
pp. 579-623 ◽  
Author(s):  
THOMAS EHRHARD
Keyword(s):  
Simple Structure ◽  
Linear Logic ◽  
Sequence Spaces ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Cartesian Closed ◽  
Linear Category ◽  
Köthe Sequence Spaces ◽  
Locally Convex ◽  
Standard Concept

We present a category of locally convex topological vector spaces that is a model of propositional classical linear logic and is based on the standard concept of Köthe sequence spaces. In this setting, the ‘of course’ connective of linear logic has a quite simple structure of a commutative Hopf algebra. The co-Kleisli category of this linear category is a cartesian closed category of entire mappings. This work provides a simple setting in which typed λ-calculus and differential calculus can be combined; we give a few examples of computations.

On the Construction of Sequence Spaces that have Schauder Bases

1966 ◽  
Vol 18 ◽  
pp. 1281-1293 ◽  
Author(s):  
William Ruckle
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Close Connection ◽  
Original Source ◽  
Schauder Bases ◽  
Bk Spaces ◽  
Made In

It is known that every Banach space which possesses a Schauder basis is essentially a space of sequences (6, Section 11.4). The primary objectives of this paper are: (1) to illustrate the close connection between sectionally bounded BK spaces and Banach spaces which have a Schauder basis, and (2) to consider some results in these theories in such a way as to render them easy and natural. In order to reach the largest number of readers we shall use (6) as the sole basis of our discussion. References to other authors are made in order to direct the reader to the original source of a theorem or to a related discussion.

scholarly journals Chaos and frequent hypercyclicity for weighted shifts

2020 ◽  
pp. 1-37
Author(s):  
STÉPHANE CHARPENTIER ◽  
KARL GROSSE-ERDMANN ◽  
QUENTIN MENET
Keyword(s):  
Difference Sets ◽  
Weighted Shift ◽  
Sequence Spaces ◽  
Hypercyclic Operators ◽  
Weighted Shifts ◽  
Banach Sequence Spaces ◽  
Frequently Hypercyclic Operators ◽  
Köthe Sequence Spaces ◽  
The Relationship ◽  
Banach Sequence

Abstract Bayart and Ruzsa [Difference sets and frequently hypercyclic weighted shifts. Ergod. Th. & Dynam. Sys.35 (2015), 691–709] have recently shown that every frequently hypercyclic weighted shift on $\ell ^p$ is chaotic. This contrasts with an earlier result of Bayart and Grivaux [Frequently hypercyclic operators. Trans. Amer. Math. Soc.358 (2006), 5083–5117], who constructed a non-chaotic frequently hypercyclic weighted shift on $c_0$ . We first generalize the Bayart–Ruzsa theorem to all Banach sequence spaces in which the unit sequences form a boundedly complete unconditional basis. We then study the relationship between frequent hypercyclicity and chaos for weighted shifts on Fréchet sequence spaces, in particular, on Köthe sequence spaces, and then on the special class of power series spaces. We obtain, rather curiously, that every frequently hypercyclic weighted shift on $H(\mathbb {D})$ is chaotic, while $H(\mathbb {C})$ admits a non-chaotic frequently hypercyclic weighted shift.

scholarly journals The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Shaoyong Zhang ◽  
Meiling Zhang ◽  
Yujia Zhan
Keyword(s):  
Fixed Point ◽  
Sequence Spaces ◽  
Point Property ◽  
Luxemburg Norm ◽  
Continuous Norm ◽  
Absolutely Continuous ◽  
Uniform Smoothness ◽  
Orlicz Sequence Spaces ◽  
Köthe Sequence Spaces ◽  
Equivalent Conditions

It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t. Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given. As a corollary, we get a criterion for nearly uniform smoothness of Orlicz sequence spaces equipped with the Luxemburg norm. Finally, the equivalent conditions of R(a,l(Φ))<1+a and RW(a,l(Φ))<1+a are given.

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